A method, apparatus, device, and storage medium for designing spectrum-compatible waveforms for a co-located MIMO radar.
By transforming the waveform optimization mathematical model of co-located MIMO radar into a neural network model training and inference process, the problem of high computational complexity in traditional methods is solved, and efficient waveform design is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XIAN UNIV OF SCI & TECH
- Filing Date
- 2026-02-03
- Publication Date
- 2026-06-02
AI Technical Summary
Traditional methods for designing spectrum-compatible waveforms for co-located MIMO radar suffer from high computational complexity due to the high dimensionality of the problem and the non-convex nature of the constraints, making it difficult to solve efficiently.
The waveform optimization mathematical model is transformed into a neural network model training and inference process. By leveraging the function computation capabilities of the neural network, an efficient approximate solution for non-convex optimization problems can be achieved.
It improves the computational efficiency of waveform design, overcomes the problems of high computational complexity and slow convergence speed of traditional optimization algorithms, and achieves more efficient waveform design.
Smart Images
Figure CN122133448A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of digital signal processing, and particularly relates to a method, apparatus, device and storage medium for designing spectrum-compatible waveforms for co-located MIMO radar. Background Technology
[0002] Co-located MIMO radar is a type of multiple-input multiple-output radar architecture. Its antenna arrangement typically involves multiple transmitting antennas and multiple receiving antennas physically concentrated in the same location or on the same platform. Each transmitting antenna simultaneously transmits different waveform signals that are orthogonal or approximately orthogonal to each other.
[0003] For the design of spectrum-compatible waveforms for co-located MIMO radar, traditional methods based on analytical derivation or iterative optimization face the problem of high computational complexity due to the high dimensionality of the problem and the non-convex nature of the constraints when solving complex non-convex optimization models that simultaneously include in-band energy suppression, integral sidelobe level constraints, and constant mode constraints. Summary of the Invention
[0004] In view of this, embodiments of the present invention provide a spectrum-compatible waveform design method, apparatus, device, and storage medium for co-located MIMO radar, which can solve the problem of high computational complexity of algorithms caused by high problem dimensionality and non-convex constraints in related technologies.
[0005] The first aspect of this invention provides a spectral-compatible waveform design method for co-located MIMO radar, comprising:
[0006] Acquire parameter information and interference information in the radar's operating environment from a co-located MIMO radar. The parameter information includes the number of antennas and the number of sampling points, including:
[0007] Acquire parameter information and interference information in the radar operating environment of a co-located MIMO radar. The parameter information includes the number of antennas and the number of sampling points. The interference information in the radar operating environment includes the spatial frequency domain information of signal-independent interference sources and the spatial domain information of strong scatterers.
[0008] Based on the parameter information, a constrained waveform optimization mathematical model is established, wherein the constrained waveform optimization mathematical model includes an objective function that minimizes the energy distribution of the waveform within the stopband, an integral sidelobe level constraint, and a constant mode constraint.
[0009] The constrained waveform optimization mathematical model is transformed into an unconstrained augmented Lagrangian function. The augmented Lagrangian function is used as the loss function of the neural network. Based on the loss function and the gradient corresponding to the loss function, an initial neural network model is trained to obtain a trained target neural network model. The target neural network model includes the weight parameters and bias parameters of each network layer.
[0010] The parameter information and interference information in the radar operating environment are used as inputs to the target neural network model, so as to generate neural network output information as the phase information of the target radar transmitted signal.
[0011] Optionally, in a first implementation of the first aspect of the present invention, training an initial neural network model based on the loss function and the gradient corresponding to the loss function to obtain a trained target neural network model includes:
[0012] Establish an initial neural network model;
[0013] The gradient is calculated based on the loss function, and the parameters of the initial neural network model are iteratively updated by the optimizer based on the gradient until the preset convergence condition is met, thereby obtaining the trained target neural network model. The set of network weights and bias parameters obtained after training constitutes the parameters of the target neural network model.
[0014] Optionally, in the second implementation of the first aspect of the invention, calculating the gradient based on the loss function includes:
[0015] The parameters of the initial neural network model are updated using the Adam optimizer based on the gradient;
[0016] After each iteration update, it is determined whether a preset convergence condition is met. The convergence condition is that the norm of the gradient is less than a set threshold.
[0017] When the convergence condition is met, the iteration is terminated, and the set of network weights and bias parameters obtained after the current iteration is used as the parameters of the trained target neural network model.
[0018] Optionally, in a third implementation of the first aspect of the present invention, the convergence condition based on the gradient includes the norm of the gradient being less than a set threshold, or the number of iterations reaching a preset maximum number of iterations.
[0019] Optionally, in a fourth implementation of the first aspect of the present invention, the initial neural network model includes an input layer, a hidden layer and an output layer connected in sequence, wherein the number of hidden layers is greater than or equal to 1.
[0020] Optionally, in a fifth implementation of the first aspect of the present invention, the hidden layer includes a first hidden layer, a second hidden layer, and a third hidden layer. The first hidden layer contains 512 nodes and uses the Swish activation function. The first hidden layer is configured with a Dropout layer with a dropout rate of 30%. The second hidden layer contains 256 nodes and uses the LeakyReLU activation function with a slope of 0.01. The third hidden layer contains 128 nodes and uses the Swish activation function.
[0021] Optionally, in a sixth implementation of the first aspect of the present invention, the hidden layer includes a first hidden layer, a second hidden layer, and a third hidden layer. The first hidden layer contains 512 nodes and uses the Swish activation function. The first hidden layer is configured with a Dropout layer with a dropout rate of 30%. The second hidden layer contains 256 nodes and uses the LeakyReLU activation function with a slope of 0.01. The third hidden layer contains 128 nodes and uses the Swish activation function.
[0022] Secondly, embodiments of the present invention provide a method and apparatus for designing spectrum-compatible waveforms for co-located MIMO radar, the apparatus comprising:
[0023] The acquisition module is used to acquire parameter information of the co-located MIMO radar and interference information in the radar operating environment. The parameter information includes the number of antennas and the number of sampling points. The interference information in the radar operating environment includes the spatial frequency domain information of signal-independent interference sources and the spatial domain information of strong scatterers.
[0024] The modeling module is used to establish a waveform optimization mathematical model based on the parameter information, wherein the waveform optimization mathematical model includes an interference region energy index, an integral sidelobe level constraint, and a constant mode constraint.
[0025] The training module is used to transform the waveform optimization mathematical model into a loss function, and train an initial neural network model according to the loss function and the gradient corresponding to the loss function to obtain a trained target neural network model, wherein the target neural network model includes weight parameters and bias parameters of each network layer;
[0026] The output module is used to take the parameter information and the interference information in the radar operating environment as input to the target neural network model, so as to generate neural network output information as the phase information of the target radar transmitted signal through the target neural network model.
[0027] Thirdly, embodiments of the present invention provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the above-described co-located MIMO radar spectrum-compatible waveform design method.
[0028] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described co-located MIMO radar spectrum-compatible waveform design method.
[0029] Fifthly, embodiments of the present invention provide a computer program product that, when run on an electronic device, causes the electronic device to execute the aforementioned spectral compatible waveform design method for co-located MIMO radar.
[0030] The beneficial effects of this invention compared to existing technologies are as follows: by transforming the solution process of a waveform optimization mathematical model containing non-convex constraints and high-dimensional variables into a neural network model training and inference process, and leveraging the function computation capabilities of the neural network, efficient approximate solutions to non-convex optimization problems can be achieved. This method enables waveform design methods to overcome the inherent defects of traditional optimization algorithms, such as high computational complexity, slow convergence speed, and even difficulty in convergence, when facing this problem, thereby improving the overall computational efficiency of waveform design. Attached Figure Description
[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0032] Figure 1 This is a schematic diagram of an embodiment of the spectrum-compatible waveform design method for a co-located MIMO radar according to the present invention.
[0033] Figure 2 This is a schematic diagram of Embodiment 2 of the spectrum-compatible waveform design method for co-located MIMO radar in this invention.
[0034] Figure 3 This is an architecture diagram of the initial neural network model in Embodiment 2 of the spectrum-compatible waveform design method for co-located MIMO radar in this invention.
[0035] Figure 4 This is a schematic diagram of an embodiment of the spectrum-compatible waveform design method device for co-located MIMO radar in this invention.
[0036] Figure 5 This is a schematic diagram of one embodiment of the electronic device in this invention. Detailed Implementation
[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are protected by this invention.
[0038] It should be noted that the terms "comprising," "including," and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this invention, are intended to cover non-exclusive inclusion. For example, a process, method, terminal, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices. In the claims, specification, and accompanying drawings of this invention, relational terms such as "first" and "second" are used merely to distinguish one entity / operation / object from another entity / operation / object, and do not necessarily require or imply any such immediate relationship or order between these entities / operations / objects.
[0039] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.
[0040] Co-located MIMO radar is a type of multiple-input multiple-output radar. Its antenna arrangement typically involves multiple transmitting antennas and multiple receiving antennas physically concentrated in the same location or on the same platform. Each transmitting antenna simultaneously transmits different waveform signals that are orthogonal or approximately orthogonal to each other.
[0041] For the waveform design problem of co-located MIMO radar, traditional methods based on analytical derivation or iterative optimization face the problem of high computational complexity due to the high dimensionality of the problem and the non-convex nature of the constraints when solving complex non-convex optimization models that simultaneously include minimizing waveform energy in the stopband, integral sidelobe level constraints, and constant mode constraints.
[0042] In view of this, embodiments of the present invention provide a spectral-compatible waveform design method, apparatus, device, and storage medium for co-located MIMO radar. By transforming the solution process of a waveform optimization mathematical model containing non-convex constraints and high-dimensional variables into a neural network model training and inference process, and leveraging the function computation capabilities of the neural network, efficient approximate solutions to the optimization problem can be achieved. This method enables waveform design to overcome the inherent defects of traditional optimization algorithms, such as high computational complexity, slow convergence speed, and even difficulty in convergence, when facing this problem, thereby improving the overall computational efficiency of waveform design.
[0043] To illustrate the technical solution of the present invention, specific embodiments are described below.
[0044] The technical terms used in the embodiments of this invention include, but are not limited to:
[0045] Co-located MIMO radar: refers to a MIMO (Multiple Input Multiple Output) radar system in which multiple transmitting antennas and multiple receiving antennas are spatially concentrated in the same location. It achieves higher waveform diversity gain and spatial degrees of freedom than traditional phased array radar by designing and transmitting mutually orthogonal or low-correlation waveforms.
[0046] Waveform optimization mathematical model: refers to the mathematical expression established to describe the design objectives and constraints for designing the transmit waveform of a MIMO radar. This model includes an objective function that needs to be minimized (or maximized), and one or more constraints that must be satisfied. In this invention, this model aims to achieve spectral compatibility performance optimization.
[0047] Spectral compatibility performance index: In this invention, it specifically refers to a quantitative index that measures the compatibility of the radar transmitted waveform with the external electromagnetic environment. Specifically, it represents the total energy generated by the radar transmitted signal within the space-frequency region where a specific interference source and strong scatterer are located. Minimizing this index is the core objective of achieving interference suppression.
[0048] The energy index of the waveform distribution within the stopband: This is a specific objective function term included in the waveform optimization mathematical model, mathematically represented as the sum of the energy distribution of the radar transmitted signal in the directions and frequency bands of signal-independent interference sources and strong scatterers. Minimizing this term maximizes the interference suppression capability.
[0049] Integral sidelobe level (ISL) constraint: A performance constraint in radar waveform design used to limit the total energy of sidelobes in the waveform's autocorrelation or cross-correlation functions. A lower ISL helps improve radar detection and resolution performance in aliasing and multi-target environments.
[0050] Constant mode constraint: A hardware limitation in radar waveform design that requires the amplitude of the transmitted waveform to be constant at each sampling point. This constraint aims to ensure that the power amplifier operates in the saturation region to achieve the highest power transmission efficiency.
[0051] Loss function: In the field of machine learning, it refers to a scalar function used to guide model training and quantify the difference between the model output and the desired target. In this invention, it specifically refers to a function that can be directly optimized by a neural network using gradient descent, derived from a waveform optimization mathematical model containing the objective function and constraints through mathematical transformations (such as the augmented Lagrangian method).
[0052] Target neural network model: refers to a neural network whose parameters have been determined and fixed through a training process. This model encapsulates the mapping relationship from a specific input to the desired output and can be used for real-time inference.
[0053] Augmented Lagrange expression: A mathematical method for solving constrained optimization problems. It integrates the constraints of the original problem into the objective function in the form of penalty terms and Lagrange multipliers, thereby transforming the constrained optimization problem into a series of unconstrained optimization problems to be solved. In this invention, this expression is used as the loss function for training a neural network.
[0054] Jacobian matrix: A matrix consisting of the first-order partial derivatives of a vector-valued function with respect to all input variables. In this invention, it specifically refers to the matrix of partial derivatives of the neural network output with respect to the neural network's own parameters, serving as an intermediate measure for calculating the gradient of the loss function with respect to the network parameters.
[0055] Adam optimizer: A stochastic optimization algorithm widely used in deep learning to iteratively update the parameters of a neural network based on calculated gradients.
[0056] Example 1:
[0057] Figure 1 This diagram illustrates a flowchart of a spectral-compatible waveform design method for a co-located MIMO radar according to an embodiment of the present invention. This method can be applied to electronic devices, such as servers, service clusters, mobile phones, tablets, laptops, ultra-mobile personal computers (UMPCs), netbooks, etc.
[0058] Specifically, the above-mentioned co-located MIMO radar spectrum compatible waveform design method may include the following steps S101 to S104.
[0059] Step S101: Obtain parameter information of the co-located MIMO radar and interference information in the radar operating environment. The parameter information includes the number of antennas and the number of sampling points. The interference information in the radar operating environment includes the spatial frequency domain information of signal-independent interference sources and the spatial domain information of strong scatterers.
[0060] In embodiments of the present invention, system parameter information of the co-located MIMO radar (including the number of antennas M and the number of sampling points N within a pulse period) and interference information sensed or preset in the radar operating environment are read from the storage module or external sensor interface. The interference information includes the spatial domain and normalized frequency band information of signal-independent interference sources, as well as the spatial location information of strong scatterers.
[0061] Step S102: Based on the parameter information, establish a constrained waveform optimization mathematical model, which includes an objective function to minimize the energy distribution of the waveform within the stopband, integral sidelobe level constraints, and constant mode constraints.
[0062] In an embodiment of the present invention, a constrained waveform optimization mathematical model is established based on the acquired parameters and interference information. The waveform optimization mathematical model takes minimizing the total energy distribution of the radar transmitted waveform in the corresponding spatial frequency domains of the interference source and the strong scatterer as the objective function, and takes the integral sidelobe level (ISL) being lower than a preset threshold and the transmitted signal satisfying the constant mode constraint (i.e., only the phase is variable and the amplitude is constant) as the constraint conditions of the model.
[0063] Optionally, the threshold value for the integral sidelobe level constraint can be set from 2N to 5N, where N is the number of sampling points. By specifically limiting the threshold value of the integral sidelobe level constraint to the range of 2N to 5N, the optimization problem can be solved, and the waveform generated by the neural network can be forced to meet an engineering-acceptable level of sidelobe suppression. This solves the problem of blindly setting constraint parameters, enabling the method to stably produce practical radar waveforms that simultaneously meet spectral compatibility requirements and low sidelobe performance.
[0064] Optionally, in a specific instance, a waveform optimization mathematical model is established that includes interference region energy indices, ISL constraints, and PAPR constraints;
[0065] Assume the radar array has M transmitting antennas, and the waveform transmitted by each antenna is as follows: , ,…, N represents the number of sampling points within a pulse period. The radar system has K signal-independent interference sources, whose actively emitted interference signals overlap with the radar's operating frequency band. Assume the... The airspace where the interference source is located , record The interference signals emitted by the interference sources are . The occupied frequency band (normalized) is denoted as Additionally, consider that the system also has Several strong scattering objects reflect radar signals; to the radar, these echoes constitute signal-correlated interference. The first... The spatial location of a strong scatterer is denoted as .
[0066] The signal energy received by the radar from the k-th signal-independent interference source is:
[0067] ;
[0068] The signal energy received by the radar from the q-th strong scatterer is
[0069] ;
[0070] in It is a direction guidance vector. It is a frequency steering vector.
[0071] The total energy of the radar waveform within the stopband can be expressed as:
[0072]
[0073] For radar signals, consider that they satisfy the following conditions:
[0074] 1. Constant modulus constraint: ;
[0075] 2. ISL constraints: .
[0076] To reduce interference, the optimization objective is set as minimizing the energy distribution of the waveform within the stopband. The optimization problem is modeled as follows:
[0077] ;
[0078] The objective function of the problem is quadratic, while constraint 2 is non-convex, making it difficult to obtain a closed-form solution. To simplify the problem, we assume... , Let be the phase of the signal from the i-th antenna at the n-th sampling point. This ensures that the signal satisfies the constant modulus constraint, thus the above optimization problem can be simplified to:
[0079] ;
[0080] The above formula is used as a mathematical model for waveform optimization.
[0081] Step S103: The constrained waveform optimization mathematical model is transformed into an unconstrained augmented Lagrangian function. The augmented Lagrangian function is used as the loss function of the neural network. Based on the loss function and the gradient corresponding to the loss function, the initial neural network model is trained to obtain the trained target neural network model. The target neural network model includes the weight parameters and bias parameters of each network layer.
[0082] In an embodiment of the present invention, a constrained optimization model is transformed into an unconstrained augmented Lagrangian function through mathematical transformation. This augmented Lagrangian function is defined as the loss function of the neural network. Then, a neural network model structure with an input layer, hidden layers, and an output layer is initialized. Based on the defined loss function, the gradient of this function with respect to the network parameters is calculated.
[0083] Based on the gradient information, the weights and bias parameters of each layer of the neural network are iteratively updated through the optimization algorithm until the training process meets the preset convergence criteria (such as the gradient norm being small enough or reaching the maximum number of iterations), thereby obtaining a set of target neural network models that have been trained and have fixed parameters.
[0084] Step S104: The parameter information and the interference information in the radar operating environment are used as inputs to the target neural network model, so as to generate the neural network output information as the phase information of the target radar transmitted signal.
[0085] In an embodiment of the present invention, during actual deployment and operation, the parameters (M, N) of the current radar system and real-time interference environment information are input as input data to the trained target neural network model. The target neural network model performs forward propagation calculations on the input data, and its output is the phase information corresponding to each antenna at each sampling time in the designed target radar transmitted signal.
[0086] The beneficial effects of this invention compared to existing technologies are as follows: by transforming the solution process of a waveform optimization mathematical model containing non-convex constraints and high-dimensional variables into a neural network model training and inference process, and leveraging the function computation capabilities of the neural network, an efficient approximate solution to the optimization problem can be achieved. This method enables waveform design methods to overcome the inherent defects of traditional optimization algorithms, such as high computational complexity, slow convergence speed, and even difficulty in convergence, when facing this problem, thereby improving the overall computational efficiency of waveform design.
[0087] Example 2:
[0088] In an optional specific embodiment of the present invention, refer to Figure 2 , Figure 2This is a schematic diagram of Embodiment 2 of the spectrum-compatible waveform design method for co-located MIMO radar in this invention. The waveform optimization mathematical model is transformed into a loss function, and an initial neural network model is trained based on the loss function and the gradient corresponding to the loss function to obtain a trained target neural network model. Specifically, it may include steps S201 to S204.
[0089] Step S201: Establish the initial neural network model.
[0090] Step S202: Calculate the gradient based on the loss function, and iteratively update the parameters of the initial neural network model through the optimizer based on the gradient until the preset convergence condition is met, thereby obtaining the trained target neural network model. The set of network weights and bias parameters obtained after training is the parameter of the target neural network model.
[0091] In an embodiment of the present invention, after each iteration, it is checked whether a preset termination condition is met.
[0092] Optionally, the termination condition can be that the number of training iterations reaches a preset maximum value.
[0093] Alternatively, the termination condition can also be that the calculated gradient norm of the loss function is less than a preset threshold, indicating that the optimization process may have approached a stationary point.
[0094] When any termination condition is met, the iterative training process stops, and the target neural network model is obtained.
[0095] Optionally, the initial neural network model includes an input layer, a hidden layer, and an output layer connected in sequence, with the number of hidden layers being greater than or equal to 1.
[0096] This optional embodiment also includes:
[0097] Step S1031: Initialize the inputs N, M, K, and Q, where N is the number of antennas, M is the number of sampling points, K is the interference source information, and Q is the strong scatterer information.
[0098] Step S1032: Construct the initial neural network model architecture, which includes an input layer, three hidden layers, and one output layer. This includes:
[0099] Input layer → Hidden layer 1 → Hidden layer 2 → Hidden layer 3 → Output layer (2×NM nodes, linear output: NM nodes). Optional, see reference. Figure 3 , Figure 3The initial neural network model architecture in this embodiment includes a first hidden layer, a second hidden layer, and a third hidden layer. The first hidden layer contains 512 nodes and uses the Swish activation function. The first hidden layer is configured with a Dropout layer with a dropout rate of 30%. The second hidden layer contains 256 nodes and uses the LeakyReLU activation function with a slope of 0.01. The third hidden layer contains 128 nodes and uses the Swish activation function.
[0100] Step S1033: Based on the above analysis, in order to solve the optimization problem, the optimization problem is described as its corresponding augmented Lagrange expression:
[0101] make , The augmented Lagrange expression for the optimization problem can then be expressed as:
[0102] ;
[0103] The input data is fed into the constructed neural network, and the loss value corresponding to the current parameter s is calculated. .
[0104] Step S1034, calculate the gradient:
[0105]
[0106] in,
[0107] ;
[0108] in, Let h be the Jacobian matrix at s.
[0109] Step S1035: Update the weights and determine the loop termination condition:
[0110] Calculate the gradient according to the gradient calculation formula, and update the neural network parameters W using the Adam optimizer;
[0111] Determine the termination condition:
[0112] ;
[0113] goto step S1036;
[0114] Else;
[0115] goto step S1033;
[0116] end if.
[0117] in, This indicates that the norm of the gradient is less than a set threshold.
[0118] This indicates that the maximum number of iterations has been reached.
[0119] Step S1036: End.
[0120] In this embodiment of the invention, an augmented Lagrangian function is used as the loss function of the neural network, and whether the constraint conditions are met is included in the criterion for training termination. This provides an end-to-end training mechanism, enabling the neural network to learn and approximate the optimal solution of a complex constrained optimization problem, thereby significantly improving the overall optimization efficiency of waveform design.
[0121] Example 3:
[0122] In an optional embodiment of the present invention, when the model training meets a preset termination condition, the model training is stopped, and the target neural network model is obtained. Specifically, this may include steps S301 to S304:
[0123] Step S301: Use the Adam optimizer to update the parameters of the initial neural network model based on the gradient.
[0124] In this embodiment of the invention, the Adam optimizer is used, taking the gradient vector calculated in the previous step as input. Internally, the Adam optimizer combines momentum and an adaptive learning rate to calculate the adjustment amount for each network parameter in the current iteration. Subsequently, the parameters of the initial neural network model are updated based on the gradient, i.e., the current parameter values are subtracted from the adjustment amount to obtain a new set of parameter values.
[0125] Step S302: After each iteration update, determine whether the preset convergence condition is met. The convergence condition is that the norm of the gradient is less than a set threshold.
[0126] In an embodiment of the present invention, after completing the parameter update, it is determined whether a preset convergence condition is met. The convergence condition is that the norm of the currently calculated gradient (e.g., the L2 norm) is less than a preset threshold. This threshold is a small positive number close to zero (e.g., 1e-6), which physically means that the slope of the loss function at the current parameter point is sufficiently gentle, indicating that the parameters may be close to a stationary point. The judgment logic is that if the gradient norm is less than the threshold, the condition is met; otherwise, it is not met.
[0127] Step S303: When the convergence condition is met, terminate the iteration and use the set of network weights and bias parameters obtained after the current iteration as the parameters of the trained target neural network model.
[0128] In an embodiment of the present invention, when the convergence condition is met, the iteration is terminated and the optimization loop is exited. The set of network weights and bias parameters that have become stable after the current iteration is saved and solidified as the parameters of the trained target neural network model.
[0129] If the convergence condition is not met, the process returns to forward propagation and gradient calculation, and the model parameters updated by backpropagation are used to start the next iteration until the convergence condition is triggered.
[0130] Optionally, convergence conditions include the gradient norm being less than a set threshold, or the number of iterations reaching a preset maximum number of iterations. The setting of reaching the preset maximum number of iterations is added as another parallel convergence condition. This provides a deterministic, anti-infinite-loop protection mechanism for the neural network training process.
[0131] In this embodiment of the invention, by limiting the use of the Adam optimizer and using the norm of the gradient being less than a set threshold as the convergence condition, more stable and faster parameter convergence can be achieved when solving the aforementioned non-convex waveform optimization problem, effectively avoiding oscillations or stagnation in the training process.
[0132] Figure 4 This diagram illustrates a structural schematic of a spectrum-compatible waveform design method apparatus for a co-located MIMO radar according to an embodiment of the present invention. The aforementioned spectrum-compatible waveform design method apparatus 700 for a co-located MIMO radar can be configured on an electronic device. Specifically, the aforementioned spectrum-compatible waveform design method apparatus 700 for a co-located MIMO radar may include:
[0133] The acquisition module 701 is used to acquire parameter information of the co-located MIMO radar and interference information in the radar operating environment. The parameter information includes the number of antennas and the number of sampling points. The interference information in the radar operating environment includes the spatial frequency domain information of signal-independent interference sources and the spatial domain information of strong scatterers.
[0134] The generation module 702 is used to establish a waveform optimization mathematical model based on parameter information. The waveform optimization mathematical model includes interference region energy index, integral sidelobe level constraint and constant mode constraint.
[0135] Training module 703 is used to transform the waveform optimization mathematical model into a loss function, and train an initial neural network model based on the loss function and the gradient corresponding to the loss function to obtain a trained target neural network model. The target neural network model includes the weight parameters and bias parameters of each network layer.
[0136] The output module 704 is used to take parameter information and interference information in the radar operating environment as input to the target neural network model, so as to generate neural network output information as the phase information of the target radar transmitted signal through the target neural network model.
[0137] The beneficial effects of this invention compared to existing technologies are as follows: by transforming the solution process of a waveform optimization mathematical model containing non-convex constraints and high-dimensional variables into a neural network model training and inference process, and leveraging the function computation capabilities of the neural network, an efficient approximate solution to the optimization problem can be achieved. This method enables waveform design methods to overcome the inherent defects of traditional optimization algorithms, such as high computational complexity, slow convergence speed, and even difficulty in convergence, when facing this problem, thereby improving the overall computational efficiency of waveform design.
[0138] Module 703 can also be specifically used for:
[0139] An initial neural network model is established using the augmented Lagrange function as the loss function.
[0140] Based on the parameter information, perform model training on the initial neural network model;
[0141] When the model training meets the preset termination condition, the model training stops, and the target neural network model is obtained.
[0142] Module 703 can also be specifically used for:
[0143] The waveform optimization mathematical model is transformed into the corresponding augmented Lagrange expression as the loss function, and an initial neural network model is established.
[0144] The gradient is calculated based on the loss function, and the parameters of the initial neural network model are iteratively updated by the optimizer based on the gradient until the preset convergence condition is met, thus obtaining the trained target neural network model. The set of network weights and bias parameters obtained after training constitutes the parameters of the target neural network model.
[0145] The cleaning module 703 can also be specifically used for:
[0146] Calculate the gradient of the loss function with respect to the neural network parameters, where the gradient is equal to the product of the gradient of the loss function with respect to the signal parameters and the transpose of the Jacobian matrix of the signal parameters with respect to the neural network output.
[0147] The calculation module 703 can also be specifically used for:
[0148] The Adam optimizer is used to update the parameters of the initial neural network model based on the gradient;
[0149] After each iteration update, it is determined whether the preset convergence condition is met. The convergence condition is that the norm of the gradient is less than a set threshold.
[0150] When the convergence condition is met, the iteration is terminated, and the set of network weights and bias parameters obtained after the current iteration is used as the parameters of the trained target neural network model.
[0151] like Figure 5 The diagram illustrates an electronic device according to an embodiment of the present invention. The electronic device 800 may include a processor 801, a memory 802, and a computer program 803 stored in the memory 802 and executable on the processor 801, such as a spectrum-compatible waveform design method program for co-located MIMO radar. When the processor 801 executes the computer program 803, it implements the steps described in the embodiments of the spectrum-compatible waveform design methods for various co-located MIMO radars.
[0152] A computer program can be divided into one or more modules / units. One or more modules / units are stored in memory 802 and executed by processor 801 to complete the present invention. One or more modules / units can be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in an electronic device.
[0153] The electronic device may include, but is not limited to, a processor 801 and a memory 802. Those skilled in the art will understand that... Figure 5 This is merely an example of an electronic device and does not constitute a limitation on the electronic device. It may include more or fewer components than shown, or combine certain components, or different components. For example, an electronic device may also include input / output devices, network access devices, buses, etc.
[0154] The processor 801 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.
[0155] The memory 802 can be an internal storage unit of an electronic device, such as a hard drive or RAM. The memory 802 can also be an external storage device of the electronic device, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card. Furthermore, the memory 802 can include both internal and external storage units. The memory 802 is used to store computer programs and other programs and data required by the electronic device. The memory 802 can also be used to temporarily store data that has been output or will be output.
[0156] It should be noted that, for the sake of convenience and brevity, the structure of the above-mentioned electronic device can also be referred to the specific description of the structure in the method embodiment, which will not be repeated here.
[0157] This invention also provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement the steps in the above-described co-located MIMO radar spectrum-compatible waveform design method.
[0158] This invention provides a computer program product that, when run on a mobile terminal, enables the mobile terminal to implement the steps in the above-described co-located MIMO radar spectrum-compatible waveform design method.
[0159] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.
[0160] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for various specific applications, but such implementations should not be considered beyond the scope of this invention.
[0161] In the embodiments provided by this invention, it should be understood that the disclosed electronic devices and methods can be implemented in other ways. For example, the electronic device embodiments described above are merely illustrative. Furthermore, the couplings or direct couplings or communication connections shown or discussed may be indirect couplings or communication connections through interfaces, devices, or units, and may be electrical, mechanical, or other forms.
[0162] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.
[0163] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.
[0164] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.
[0165] The embodiments described above are merely illustrative of the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. These modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.
Claims
1. A spectral-compatible waveform design method for a co-located MIMO radar, characterized in that, include: Acquire parameter information and interference information in the radar operating environment of a co-located MIMO radar. The parameter information includes the number of antennas and the number of sampling points. The interference information in the radar operating environment includes the spatial frequency domain information of signal-independent interference sources and the spatial domain information of strong scatterers. Based on the parameter information, a constrained waveform optimization mathematical model is established, wherein the constrained waveform optimization mathematical model includes an objective function that minimizes the energy distribution of the waveform within the stopband, an integral sidelobe level constraint, and a constant mode constraint. The constrained waveform optimization mathematical model is transformed into an unconstrained augmented Lagrangian function. The augmented Lagrangian function is used as the loss function of the neural network. Based on the loss function and the gradient corresponding to the loss function, an initial neural network model is trained to obtain a trained target neural network model. The target neural network model includes the weight parameters and bias parameters of each network layer. The parameter information and interference information in the radar operating environment are used as inputs to the target neural network model, so as to generate neural network output information as the phase information of the target radar transmitted signal.
2. The spectral-compatible waveform design method for co-located MIMO radar as described in claim 1, characterized in that, Based on the loss function and its corresponding gradient, an initial neural network model is trained to obtain a trained target neural network model, including: Establish an initial neural network model; The gradient is calculated based on the loss function, and the parameters of the initial neural network model are iteratively updated by the optimizer based on the gradient until the preset convergence condition is met, thereby obtaining the trained target neural network model. The set of network weights and bias parameters obtained after training constitutes the parameters of the target neural network model.
3. The spectral-compatible waveform design method for co-located MIMO radar as described in claim 2, characterized in that, The step of iteratively updating the parameters of the initial neural network model using an optimizer based on the gradient until a preset convergence condition is met, thereby obtaining the trained target neural network model, includes: The parameters of the initial neural network model are updated using the Adam optimizer based on the gradient; After each iteration update, it is determined whether a preset convergence condition is met. The convergence condition is that the norm of the gradient is less than a set threshold. When the convergence condition is met, the iteration is terminated, and the set of network weights and bias parameters obtained after the current iteration is used as the parameters of the trained target neural network model.
4. The spectral-compatible waveform design method for co-located MIMO radar as described in claim 3, characterized in that, The convergence conditions include the norm of the gradient being less than a set threshold, or the number of iterations reaching a preset maximum number of iterations.
5. The spectral-compatible waveform design method for co-located MIMO radar as described in any one of claims 1 to 4, characterized in that, The initial neural network model includes an input layer, a hidden layer, and an output layer connected in sequence, wherein the number of hidden layers is greater than or equal to 1.
6. The spectral-compatible waveform design method for co-located MIMO radar as described in claim 5, characterized in that, The hidden layer includes a first hidden layer, a second hidden layer, and a third hidden layer. The first hidden layer contains 512 nodes and uses the Swish activation function. The first hidden layer is configured with a Dropout layer with a dropout rate of 30%. The second hidden layer contains 256 nodes and uses the LeakyReLU activation function with a slope of 0.
01. The third hidden layer contains 128 nodes and uses the Swish activation function.
7. The spectral-compatible waveform design method for co-located MIMO radar as described in claim 1, characterized in that, The threshold value of the integral sidelobe level constraint ranges from 2N to 5N, where N is the number of sampling points.
8. A method and apparatus for designing spectral-compatible waveforms for co-located MIMO radar, characterized in that, The device includes: The acquisition module is used to acquire parameter information of the co-located MIMO radar and interference information in the radar operating environment. The parameter information includes the number of antennas and the number of sampling points. The interference information in the radar operating environment includes the spatial frequency domain information of signal-independent interference sources and the spatial domain information of strong scatterers. The modeling module is used to establish a waveform optimization mathematical model based on the parameter information, wherein the waveform optimization mathematical model includes an interference region energy index, an integral sidelobe level constraint, and a constant mode constraint. The training module is used to transform the waveform optimization mathematical model into a loss function, and train an initial neural network model according to the loss function and the gradient corresponding to the loss function to obtain a trained target neural network model, wherein the target neural network model includes weight parameters and bias parameters of each network layer; The output module is used to take the parameter information and the interference information in the radar operating environment as input to the target neural network model, so as to generate neural network output information as the phase information of the target radar transmitted signal through the target neural network model.
9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the spectrum-compatible waveform design method for the co-located MIMO radar as described in any one of claims 1 to 7.
10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the spectrum-compatible waveform design method for the co-located MIMO radar as described in any one of claims 1 to 7.